AN INTRODUCTION TO FLUID DYNAMICSPDF|Epub|txt|kindle电子书版本下载

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Chapter 1. The Physical Properties of Fluids1

1.1 Solids， liquids and gases1

1.2 The continuum hypothesis4

1.3 Volume forces and surface forces acting on a fluid7

Representation of surface forces by the stress tensor9

The stress tensor in a fluid at rest12

1.4 Mechanical equilibrium of a fluid14

A body ‘floating’ in fluid at rest16

Fluid at rest under gravity18

1.5 Classical thermodynamics20

1.6 Transport phenomena28

The linear relation between flux and the gradient of a scalar intensity30

The equations for diffusion and heat conduction in isotropic media at rest32

Molecular transport of momentum in a fluid36

1.7 The distinctive properties of gases37

A perfect gas in equilibrium38

Departures from the perfect-gas laws45

Transport coefficients in a perfect gas47

Other manifestations of departure from equilibrium of a perfect gas50

1.8 The distinctive properties of liquids53

Equilibrium properties55

Transport coefficients57

1.9 Conditions at a boundary between two media60

Surface tension60

Equilibrium shape of a boundary between two stationary fluids63

Transition relations at a material boundary68

Chapter 2. Kinematics of the Flow Field71

2.1 Specification of the flow field71

Differentiation following the motion of the fluid72

2.2 Conservation of mass73

Use of a stream function to satisfy the mass-conservation equation75

2.3 Analysis of the relative motion near a point79

Simple shearing motion83

2.4 Expression for the velocity distribution with specified rate of expansion and vorticity84

2.5 Singularities in the rate of expansion. Sources and sinks88

2.6 The vorticity distribution92

Line vortices93

Sheet vortices96

2.7 Velocity distributions with zero rate of expansion and zero vorticity99

Conditions for ▽φ to be determined uniquely102

Irrotational solenoidal flow near a stagnation point105

The complex potential for irrotational solenoidal flow in two dimensions106

2.8 Irrotational solenoidal flow in doubly-connected regions of space108

Conditions for ▽φ to be determined uniquely112

2.9 Three-dimensional flow fields extending to infinity114

Asymptotic expressions for uoand uv114

The behaviour of φ at large distances117

Conditions for ▽φ to be determined uniquely119

The expression of φ as a power series120

Irrotational solenoidal flow due to a rigid body in translational motion122

2.10 Two-dimensional flow fields extending to infinity124

Irrotational solenoidal flow due to a rigid body in translational motion128

Chapter 3. Equations Governing the Motion of a Fluid131

3.1 Material integrals in a moving fluid131

Rates of change of material integrals133

Conservation laws for a fluid in motion135

3.2 The equation of motion137

Use of the momentum equation in integral form138

Equation of motion relative to moving axes139

3.3 The expression for the stress tensor141

Mechanical definition of pressure in a moving fluid141

The relation between deviatoric stress and rate-of-strain for a Newtonian fluid142

The Navier-Stokes equation147

Conditions on the velocity and stress at a material boundary148

3.4 Changes in the internal energy of a fluid in motion151

3.5 Bernoulli’s theorem for steady flow of a frictionless non-conducting fluid156

Special forms of Bernoulli’s theorem161

Constancy of H across a transition region in one-dimensional steady flow163

3.6 The complete set of equations governing fluid flow164

Isentropic flow165

Conditions for the velocity distribution to be approximately solenoidal167

3.7 Concluding remarks to chapters 1，2 and 3171

Chapter 4. Flow of a Uniform Incompressible Viscous Fluid174

4.1 Introduction174

Modification of the pressure to allow for the effect of the body force176

4.2 Steady unidirectional flow179

Poiseuille flow180

Tubes of non-circular cross-section182

Two-dimensional flow182

A model of a paint-brush183

A remark on stability185

4.3 Unsteady unidirectional flow186

The smoothing-out of a discontinuity in velocity at a plane187

Plane boundary moved suddenly in a fluid at rest189

One rigid boundary moved suddenly and one held stationary190

Flow due to an oscillating plane boundary191

Starting flow in a pipe193

4.4 The Ekman layer at a boundary in a rotating fluid195

The layer at a free surface197

The layer at a rigid plane boundary199

4.5 Flow with circular streamlines201

4.6 The steady jet from a point source of momentum205

4.7 Dynamical similarity and the Reynolds number211

Other dimensionless parameters having dynamical significance215

4.8 Flow fields in which inertia forces are negligible216

Flow in slowly-varying channels217

Lubrication theory219

The Hele-Shaw cell222

Percolation through porous media223

Two-dimensional flow in a corner224

Uniqueness and minimum dissipation theorems227

4.9 Flow due to a moving body at small Reynolds number229

A rigid sphere230

A spherical drop of a different fluid235

A body of arbitrary shape238

4.10 Oseen’s improvement of the equation for flow due to moving bodies at small Reynolds number240

A rigid sphere241

A rigid circular cylinder244

4.11 The viscosity of a dilute suspension of small particles246

The flow due to a sphere embedded in a pure straining motion248

The increased rate of dissipation in an incompressible suspension250

The effective expansion viscosity of a liquid containing gas bubbles253

4.12 Changes in the flow due to moving bodies as R increases from I to about Ioo255

Chapter 5. Flow at Large Reynolds Number：Effects of Viscosity264

5.1 Introduction264

5.2 Vorticity dynamics266

The intensification of vorticity by extension of vortex-lines270

5.3 Kelvin’s circulation theorem and vorticity laws for an inviscid fluid273

The persistence of irrotationality276

5.4 The source of vorticity in motions generated from rest277

5.5 Steady flows in which vorticity generated at a solid surface is prevented by convection from diffusing far away from it282

（a） Flow along plane and circular walls with suction through the wall282

（b） Flow toward a ‘stagnation point’ at a rigid boundary285

（c） Centrifugal flow due to a rotating disk290

5.6 Steady two-dimensional flow in a converging or diverging channel294

Purely convergent flow297

Purely divergent flow298

Solutions showing both outflow and inflow301

5.7 Boundary layers302

5.8 The boundary layer on a flat plate308

5.9 The effects of acceleration and deceleration of the external stream314

The similarity solution for an external stream velocity proportional to xm316

Calculation of the steady boundary layer on a body moving through fluid318

Growth of the boundary layer in initially irrotational flow321

5.10 Separation of the boundary layer325

5.11 The flow due to bodies moving steadily through fluid331

Flow without separation332

Flow with separation337

5.12 Jets， free shear layers and wakes343

Narrow jets343

Free shear layers346

Wakes348

5.13 Oscillatory boundary layers353

The damping force on an oscillating body355

Steady streaming due to an oscillatory boundary layer358

Applications of the theory of steady streaming361

5.14 Flow systems with a free surface364

The boundary layer at a free surface364

The drag on a spherical gas bubble rising steadily through liquid367

The attenuation of gravity waves370

5.15 Examples of use of the momentum theorem372

The force on a regular array of bodies in a stream372

The effect of a sudden enlargement of a pipe373

Chapter 6. Irrotational Flow Theory and its Applications378

6.1 The role of the theory of flow of an inviscid fluid378

6.2 General properties of irrotational flow380

Integration of the equation of motion382

Expressions for the kinetic energy in terms of surface integrals383

Kelvin’s minimum energy theorem384

Positions of a maximum of q and a minimum of P384

Local variation of the velocity magnitude386

6.3 Steady flow： some applications of Bernoulli’s theorem and the momentum theorem386

Efflux from a circular orifice in an open vessel387

Flow over a weir391

Jet of liquid impinging on a plane wall392

Irrotational flow which may be made steady by choice of rotating axes396

6.4 General features of irrotational flow due to a moving rigid body398

The velocity at large distances from the body399

The kinetic energy of the fluid402

The force on a body in translational motion404

The acceleration reaction407

The force on a body in accelerating fluid409

6.5 Use of the complex potential for irrotational flow in two dimensions409

Flow fields obtained by special choice of the function w（x）410

Conformal transformation of the plane of flow413

Transformation of a boundary into an infinite straight line418

Transformation of a closed boundary into a circle420

The circle theorem422

6.6 Two-dimensional irrotational flow due to a moving cylinder with circulation423

A circular cylinder424

An elliptic cylinder in translational motion427

The force and moment on a cylinder in steady translational motion433

6.7 Two-dimensional aerofoils435

The practical requirements of aerofoils435

The generation of circulation round an serofoil and the basis for Joukowski’s hypothesis438

Aerofoils obtained by transformation of a circle441

Joukowaki aerofoils444

6.8 Axisymmetric irrotational flow due to moving bodies449

Generalities449

A moving sphere452

Ellipsoids of revolution455

Body shapes obtained from source singularities on the axis of symmetry458

Semi-infinite bodies460

6.9 Approximate results for slender bodies463

Slender bodies of revolution463

Slender bodies in two dimensions466

Thin aerofoils in two dimensions467

6.10 Impulsive motion of a fluid471

Impact of a body on a free surface of liquid473

6.11 Large gas bubbles in liquid474

A spherical-cap bubble rising through liquid under gravity475

A bubble rising in a vertical tube477

A spherical expanding bubble479

6.12 Cavitation in a liquid481

Examples of cavity formation in steady flow482

Examples of cavity formation in unsteady flow485

Collapse of a transient cavity486

Steady-state cavities491

6.13 Free-streamline theory， and steady jets and cavities493

Jet emerging from an orifice in two dimensions495

Two-dimensional flow past a flat plate with a cavity at ambient pressure497

Steady-state cavities attached to bodies held in a stream of liquid502

Chapter 7. Flow of Effectively Inviscid Fluid with Vorticity507

7.1 Introduction507

The self-induced movement of a line vortex509

The instability of a sheet vortex511

7.2 Flow in unbounded fluid at rest at infinity517

The resultant force impulse required to generate the motion518

The total kinetic energy of the fluid520

Flow with circular vortex-lines521

Vortex rings522

7.3 Two-dimensional flow in unbounded fluid at rest at infinity527

Integral invariants of the vorticity distribution528

Motion of a group of point vortices530

Steady motions532

7.4 Steady two-dimensional flow with vorticity throughout the fluid536

Uniform vorticity in a region bounded externally538

Fluid in rigid rotation at infinity539

Fluid in simple shearing motion at infinity541

7.5 Steady axisymmetric flow with swirl543

The effect of a change of cross-section of a tube on a stream of rotating fluid546

The effect of a change of external velocity on an isolated vortex550

7.6 Flow systems rotating as a whole555

The restoring effect of Coriolis forces555

Steady flow at small Rossby number557

Propagation of waves in a rotating fluid559

Flow due to a body moving along the axis of rotation564

7.7 Motion in a thin layer on a rotating sphere567

Geostrophic flow571

Flow over uneven ground573

Planetary waves577

7.8 The vortex system of a wing580

General features of the flow past lifting bodies in three dimensions580

Wings of large aspect ratio， and ‘lifting-line’ theory583

The trailing vortex system far downstream589

Highly swept wings591

Appendices594

1 Measured values of some physical properties of common fluids594

（a） Dry air at a pressure of one atmosphere594

（b） The Standard Atmosphere595

（c） Pure water595

（d） Diffusivities for momentum and heat at 15 ℃ and I atm597

（e） Surface tension between two fluids597

2 Expressions for some common vector differential quantities in orthogonal curvilinear co-ordinate systems598

Publications referred to in the text604

Subject Index609